Heat a large skillet over medium-high heat. Sprinkle fish with 1/4 teaspoon salt and pepper. Add butter to pan; swirl until butter melts. Add fish; cook 1 minute. Add wine; cover, reduce heat to medium-low, and cook 7 minutes or until fish flakes easily when tested with a fork.
Heat a small skillet over high heat. Combine tomatoes and oil. Add to pan; cook 3 minutes or until lightly charred and beginning to soften.
Place 1 fillet in each of 4 shallow bowls; spoon cooking liquid evenly over fillets. Divide tomatoes among servings. Sprinkle with 1/4 teaspoon salt and dill. Garnish with oregano, if desired.
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This was so easy and delicious. My husband took one bite and said, "Sometimes the dishes with the simplest ingredients are the best." My teenager even loved it. Too bad halibut is so expensive or I'd make this every week. I found a nice mixture of variable colored cherry tomatoes at Costco - worked perfectly. We had it with saffron rice and steamed broccoli. Will definitely make this again.
This was fabulous!! I made it the other night for my neighbor and she loved it too! The halibut was cooked perfectly this way, nice and delicate. I served it with a Kashi pilaf that I made up. It was excellent and I can't wait to make it again soon!